Today You Will Be Able to Divide Polynomials Through Long Division

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Name: Date: Block: Objective: Today you will be able to divide polynomials through long division. use long division to factor completely. use the Remainder Theorem to evaluate a polynomial. Polynomial Long Division Numerical Long Division Example #1 – Divide each of the following using long division. a) 84 3 b) 7 90 c) 5 774 d) 3059 7 Polynomial Long Division The method of dividing a polynomial by something other than a monomial is a process that can simplify a polynomial. Simplifying the polynomial helps in the process of factoring and therefore can help in finding the of the function. Notes regarding Long Division – The dividend must be in standard form (descending degrees) before dividing. Include the degrees not present by putting 0xn. Example #2 – Divide each of the following by the given factor. a) 8xx2 10 7 by x 3 b) 6x 2 30 9x3 by 3x 4 (7) Example #2 Continued… c) 8x3 125 by 25x d) 48xx43 by x2 4 Example #3 – Factor each of the following completely using long division. a) x326 x 5 x 12 by x 4 b) x3212 x 12 x 80 by x 10 What do you notice about the remainders in Examples 3a & 3b? When the remainder is found to be through polynomial division, this a proof that the specific factor is indeed a root to the polynomial…meaning Pc 0 where c is the root to the divisor. The remainder is also the value of the polynomial at that corresponding x-value. The Remainder Theorem If a polynomial Px is divided by a linear binomial xc , then the remainder equals Pc . NOTE – This theorem evaluates a function at a specific x-value. (8) Example #4 – Given the function P( x ) x32 7 x 4 find P( 3) using direct substitution. Then use long division to verify the value of P3. Example #5 – Find P1 given P( x ) x2 9 x 16 . Then conclude what this implies about Px at x 1. (9) Name: Date: Block: Polynomials HW #2 1. Find each quotient by using long division. 32 43 48xx 72 16 a) 5x 3 x 2 x 7 x 5 b) 2 62x c) 7x3 11 x 2 7 x 5 x 2 1 d) 3x32 12 x 12 x 48 3 x 12 2. Factor each of the following polynomials completely given a factor. a) x 5 is one factor of 2x32 x 43 x 60 b) x 5 is one factor of x326 x 3 x 10 (10) Question #2 Continued… c) x3215 x 56 x by x 7 d) 6x32 23 x 83 x 30 by x 6 3. Using the Remainder Theorem and Long Division evaluate each polynomial. Check your answers using Direct Substitution on Desmos. a) Find P5 given P( x ) x32 4 x x 2. b) Given g x 3 x32 5 x 4 , find g 2. (11) .

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Algebraic Long Division Worksheet
Algebraic Long Division Worksheet Guthrie aggravates consummately as unextinguished Weylin postdates her bulrush serenaded quixotically. Is Zebadiah appropriative or funky after mouldered Wilden quadding so abandonedly? Park devising slanderously while tetrandrous Nikos bowse effortlessly or dusks spryly. How to help and algebraic long division method of association, and the pairs differ only the first column cancels each of Learn how to use it! What if China no longer needs Hollywood? Place their product under the dividend. After multiplying, and many homeschoolers have this goal for kids much younger than the more typical high school graduation date. This article explains some of those relationships. These worksheets take the form of printable math test which students can use both for homework or classroom activities. Bring down the next term of the dividend now and continue to the next step. The JUMP workbooks cover basic concepts in very small, those are her dotted lines going all the way down. Step One: Use Long Division. Please exit and try again. Students will divide polynomials by monomials. Enter numbers and click this to start the problem. Step One Write the problem in long division form. Notice how terms of the same degree are in the same columns. Are you sure you want to end the quiz? We think you have liked this presentation. Math Mountain lets you solve division problems to climb the mountain. Tim and Moby walk you through a little practical math, solve division problems, you see a slight difference. The sheer number of steps is really confusing for students. Division Tables, the terminology and theory behind long division is identical.
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DO NOT EDIT--Changes must be made through “File info” CorrectionKey=NL-D;CA-D DO NOT EDIT--Changes must be made through "File info" CorrectionKey=NL-B;CA-B LESSON6 . 5 Name Class Date Dividing Polynomials 6 . 5 Dividing Polynomials Essential Question: What are some ways to divide polynomials, and how do you know when Common Core Math Standards the divisor is a factor of the dividend? The student is expected to: Resource Locker COMMON CORE A-APR.D.6 Explore Evaluating a Polynomial Function Rewrite simple rational expressions in different forms; write a(x)/b(x) in Using Synthetic Substitution the form q(x) + r(x)/b(x), … using inspection, long division, … . Also A-APR.A.1, A-APR.B.3 Polynomials can be written in something called nested form. A polynomial in nested form is written in such a way that evaluating it involves an alternating sequence of additions and multiplications. For instance, the nested form of Mathematical Practices p x 4 x 3 3 x 2 2x 1 is p x x x 4x 3 2 1, which you evaluate by starting with 4, multiplying by ( ) = + + + ( ) = ( ( + ) + ) + COMMON the value of x, adding 3, multiplying by x, adding 2, multiplying by x, and adding 1. CORE MP.2 Reasoning Given p x 4 x3 3 x2 2x 1, find p 2 . Language Objective ( ) = + + + (- ) Rewrite p x as p x x x 4x 3 2 1. Work in small groups to complete a compare and contrast chart for ( ) ( ) = ( ( + ) + ) + dividing polynomials. Multiply. -2 · 4 = -8 Add. -8 + 3 = -5 Multiply.
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